There are growing numbers of experimental evidences that the self-field critical currents, [Formula: see text], are a new instructive tool to investigate fundamental properties of superconductors ranging from atomically thin films [M. Liao et al., Nat. Phys. 6 (2018), https://doi.org/10.1038/s41567-017-0031-6 ; E. F. Talantsev et al., 2D Mater. 4 (2017) 025072; A. Fete et al., Appl. Phys. Lett. 109 (2016) 192601] to millimeter-scale samples [E. F. Talantsev et al., Sci. Rep. 7 (2017) 10010]. The basic empirical equation which quantitatively accurately described experimental [Formula: see text] was proposed by Talantsev and Tallon [Nat. Commun. 6 (2015) 7820] and it was the relevant critical field (i.e. thermodynamic field, [Formula: see text], for type-I and lower critical field, [Formula: see text], for type-II superconductors) divided by the London penetration depth, [Formula: see text]. In this paper, we report new findings relating to this empirical equation. It is that the critical wavelength of the de Broglie wave, [Formula: see text], of the superconducting charge carrier which within a numerical pre-factor is equal to the largest of two characteristic lengths of Ginzburg–Landau theory, i.e. the coherence length, [Formula: see text], for type-I superconductors or the London penetration depth, [Formula: see text], for type-II superconductors. We also formulate a microscopic criterion for the onset of dissipative transport current flow: [Formula: see text], where [Formula: see text] is the charge carrier momentum, [Formula: see text] is Planck’s constant and the inequality sign “[Formula: see text]” is reserved for the dissipation-free flow.
Probing the pinning landscape in type-II superconductors via Campbell penetration depth
